We show that the string representation of the QCD2 partition function
satisfies, by virtue of a Young-tableau-transposition symmetry, the to
pological constraint that any branched covering of an orientable or no
norientable surface without boundary must have an even branch point mu
ltiplicity. This statement holds for each chiral sector and requires m
ultiple branch point behavior for the twist points, since cross-terms
appear that couple twist points with odd powers of simple branch point
s. We obtain the same result for the complete partition function of 50
(N) and Sp(N) Yang-Mills theory.